Which description best explains the domain of (g circle f) (x)? A) the elements in the domain of f(x) for which g(f(x)) is defined
B) the elements in the domain of f(x) for which g(f(x)) is not zero
C) the elements in the domain of g(x) for which g(f(x)) is defined
D) the elements in the domain of g(x) for which g(f(x)) is not zero

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  A) the elements in the domain of f(x) for which g(f(x)) is defined

Step-by-step explanation:

(g circle f)(x) means g(f(x)). In order for a value (x) to be in the domain of this function, f(x) must be defined. That is, x must be in the domain of f(x). In addition, g(f(x)) must be defined.

These requirements are expressed in choice A.

region b will make the inequalities y < 2x + 1 and y > -x - 2 true ⇒ answer a

step-by-step explanation:

* lets study the graph and the inequality to solve the question

- the inequality y > -x - 2

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = -2 that means the line intersect the y-axis at point (0 , -2)

∵ the sign of the inequality is >

∴ we shad the part over the line

  region a and b

- the inequality y < 2x + 1

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = 1 that means the line intersect the y-axis at point (0 , 1)

∵ the sign of the inequality is <

∴ we shad the part under the line

  region b and c

∵ the common region between the two lines is region b

∴ region b will make the inequalities y < 2x + 1 and y > -x - 2 true